Research Article
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Analysis of students’ mathematical connection abilities in solving problem of circle material: transposition study

Year 2020, , 829 - 842, 15.06.2020
https://doi.org/10.17478/jegys.689673

Abstract

This study aims to describe the ability of students' mathematical connections in solving problems in the circle equation material through transposition studies. The method in this research is a descriptive qualitative approach, the techniques used in the study are tests, interviews, and documentation to explore data in research. Test and interview techniques were carried out in order to find out more about the ability of connections and generate knowledge about the transposition in making mathematical problem solving designs. The test is given to 3 students who have high ability, medium ability and low ability. Analysis of the data in this study is through the provision of problem solving tests and interviews using time triangulation, which provides tests and interviews for each student with a different time. The results in this study indicate that highly capable subjects have excellent mathematical connections and didactic knowledge is well utilized and able to provide alternative answers that differ from researchers so that a didactic transposition is formed, that is knowledge to be taught with knowledge, subjects of mathematical ability are able understand the problem well but are not careful enough in solving problem so that previous knowledge is underutilized, the subject of low mathematical ability is not able to understand the problem well and is unable to solve problems in the form of algebra so that the initial knowledge possessed is not well connected.

Supporting Institution

Indonesian Education University and STKIP Taman Siswa Bima

Project Number

082340516464

References

  • Bell, F. H. (1978). Teaching and Learning Mathematics in Secondary School. (C. Kedua (ed.)). Cetakan Kedua. Dubuque, Iowa: Wm. C. Brown Company Publishers.
  • Bergeson, T. (2000). Teaching and Learning Mathematics. Using Research to Shift From The “Yesterday” Mind to the “Tomorrow” Mind, 37. www.k12.wa.us.
  • Bingölbali, E., & Coşkun, M. 2016. A proposed conceptual framework for enhancing the use of making connections skill in mathematics teaching. Eğitim ve Bilim, 41(183), 233-249. https://doi.org/10.15390/EB.2016.4764
  • Bosch, M., & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58(58), 51–65.
  • Bosse, M. J. (2003). The beauty of “and” and “or”: connections with in mathematics for students with learning differences. Mathematics and Computer Education, 37(1), 105-114. 37(1), 105.
  • Charles, R & O’Daffer, P. (1997). How to Evaluate Progress in Problem Solving. NCTM. Reston, VA. https://www.amazon.com/Evaluate-Progress-Problem-Solving-NCTM/dp/0873532414
  • Chevallard, Y. (1989). On didactic transposition theory: Some Introductory Notes. Paper Presented at the International Symposium on Research and Development in Mathematics Education. Bratislava.
  • Chevallard, Y. (2013). Didactic Transposition in Mathematics Education. In Encyclopedies of Mathematics Education.
  • Clement, J. (2006). Designing classroom thought experiments: what we can learn from imagery indicators and expert protocols. NARST. SanFransisco. http://people.umass.edu/~clement/pdf/StephensClemDesignClssrmTE.pdf
  • Creswell, J. (2012). Research Design. Pustaka Pelajar.
  • David, H. (2015). The PISA Results in mathematics and science: A comparison between Israel and Turkey. Journal for the Education of Gifted Young Scientists, 3(1), 22-28.
  • Depdiknas. (2006). Kurikulum 2006: Standar Isi Mata Pelajaran Matematika untuk SMP/MTs. Ditjen Dikdasmen.
  • Diana, N., & Suryadi, D. (2020). Students ’ creative thinking skills on the circle subject in terms of learning obstacle and learning trajectory Students ’ creative thinking skills on the circle subject in terms of learning obstacle and learning trajectory. https://doi.org/10.1088/1742-6596/1521/3/032084
  • French, D. (2004). Teaching and Learning Geometry. Issues and Methods in Mathematical Education. London New York: Continuum., 119.
  • Gantert, A. X. (2008). Geometry. AMSCO School Publication, INC.
  • Gardner, H. (1983). Frames of mind. HarperCollins Publishers.
  • Getzels, Jacob W.; Jackson, P. W. (1962). Creativity and Intelligence: Explorations with Gifted Students. American Psychological Assosiation, 17, 293.
  • Hadi, S. dan Fauzan, A. (2003). Mengapa PMRI? Dalam Buletin PMRI (Pendidikan Matematika Realistik Indonesia). edisi I, J.
  • Harel, G. (2008). What Is Mathematics? A Pedagogical Answer to a Philosophical Question. ( PP 1-26) Washington: The Mathematical Association of America, Inc.
  • Hendriana, H & Sumarmo, U. (2014). nilaian Pembelajaran Matematika. Refika Aditaama.
  • Hodgson, T. (1995). “Connection as Problem-Solving Tools”, dalam Connecting Mathematics across the Curriculum. Editor: House, P.A. Dan Coxford, A.F. Reston, Virginia: NCTM.
  • Idris, N. (2011). The Impact of Using Geometers’ Sketchpad on Malaysia Students’ Achievement and Van Hiele Geometric Thingking Malaya. Journal for Mathematics Education Vol.2, No.2 Pp 94-107. University of Malaya, 2.
  • Johnson, K.M. dan Litynsky, C. L. (1995). Breathing Life into Mathematics, dalam Connecting Mathematics across the Curriculum. (V. N. Editor: House, P.A. dan Coxford, A.F. Reston (ed.)).
  • Kaur, B., & Lam, T. T. (2012). Reasoning, coummunication and connection in mathematics. World Scientific Publishing.
  • Kusmanto, H., & Marliyana, I. (2014). Pengaruh Pemahaman Matematika Terhadap Kemampuan Koneksi Matematika Siswa Kelas Vii Semester Genap Smp Negeri 2 Kasokandel Kabupaten Majalengka. Eduma : Mathematics Education Learning and Teaching, 3(2). https://doi.org/10.24235/eduma.v3i2.56
  • Lattery, M. (2001). Thought Experiments in PhysicsEducation: A Simple and Practical Example. Science and Education, 10(5), 485-92.
  • Lexy J. Moleong. (2011). Metodologi penelitian kualitatif. Bandung: Remaja Rosdakarya.
  • Maker, C. J. (1982). Curriculum development for the gifted. Rockville, Md.: Aspen Systems Corp.
  • Maker, C. J. (2004). Creativity and multiple intelligences: The DISCOVER project and research. In S. Lau, A. N. N. Hui, & G. Y. C. Ng (Eds.), Creativity: When East meets West. (pp. 341‐392). Singapore: World Scientific.
  • Maker, J., & Zimmerman, R., Alhusaini, A., & Pease, R. (2015). Real Engagement in Active Problem Solving (REAPS): An evidencebased model that meets content, process, product, and learning environment principles recommended for gifted students. APEX: The New Zealand Journal of Gifted Education, 19(1). Retrieved from www.giftedchildren.org.nz/apex.
  • Miles dan Huberman. (1992). Analisis data Kualitatif. Jakarta : UI Press.
  • Mousley, J. (2004). An aspect of mathematical understanding: the notion of “connected knowing”. Proceedings of the 28th Conference of the International Groupforthe Psychology of Mathematics Education, 3-25, 377-384.
  • NCTM. (2000). Principles and Standards for School Mathematics. www.nctm.org
  • Özgen, K. (2013). Self efficacy beliefs in mathematical literacy and connectiona between mathematics and real world : the case of high school students. Journal of International Education Research. 4(9).
  • Recegnova, M. (2005). Teaching of Analytic Geometry an vector calculus and proposals of problems’ solutions. ActaDidactica Universitatis Comenianae., Mathematics, Issue 5, 2005.
  • Romli, M. (2016). Profil Koneksi Matematis Siswa Perempuan SMA dengan Kemampuan Matematika Tinggi dalam Menyelesaikan Masalah Matematika. MUST: Journal of Mathematics Education, Science and Technology, 1(2), 144. https://doi.org/10.30651/must.v1i2.234
  • Saragih, M. . (2008). Rancangan dan Implementasi Program Perangkat Ajar serta Rancangan Materi Perangkat Ajar Geometri SMU Kelas I Berbantuan Komputer. Forum Penelitian Pendidikan, Thn 8.
  • Tortop, S. H. (2016). Why thought experiments should be used as an educational tool to develop problem solving skills and creativity of the gifted students. Journal of Gifted Educational and Creativity, 35-48.
  • Tortop, H. S. (2018). Üstün zekâlılar eğitiminde farklılaştırılmışöğretim, müfredat farklılaştırma modelleri [Differentiated instruction for gifted, curriculum differentiation models in gifted education]. Istanbul: Young Wise Publishing
  • Travers. (1987). Geometry. Laidlaw Brothers Publisher. River Forest Illinois.
  • Turmudi. (2010). Pembelajaran Matematika Kini dan Kencenderungan Masa Mendatang. Buku Bunga Rampai Pembelajaran MIPA, JICA FPMIPA.
  • Turnuklu, E., & Yesildere, S. (2007). The Pedagogical Content Knowledge in Mathematics: Pre-Service Primary Mathematics Teachers’ Perspectives in Turkey. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1(October), 1–13.
Year 2020, , 829 - 842, 15.06.2020
https://doi.org/10.17478/jegys.689673

Abstract

Project Number

082340516464

References

  • Bell, F. H. (1978). Teaching and Learning Mathematics in Secondary School. (C. Kedua (ed.)). Cetakan Kedua. Dubuque, Iowa: Wm. C. Brown Company Publishers.
  • Bergeson, T. (2000). Teaching and Learning Mathematics. Using Research to Shift From The “Yesterday” Mind to the “Tomorrow” Mind, 37. www.k12.wa.us.
  • Bingölbali, E., & Coşkun, M. 2016. A proposed conceptual framework for enhancing the use of making connections skill in mathematics teaching. Eğitim ve Bilim, 41(183), 233-249. https://doi.org/10.15390/EB.2016.4764
  • Bosch, M., & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58(58), 51–65.
  • Bosse, M. J. (2003). The beauty of “and” and “or”: connections with in mathematics for students with learning differences. Mathematics and Computer Education, 37(1), 105-114. 37(1), 105.
  • Charles, R & O’Daffer, P. (1997). How to Evaluate Progress in Problem Solving. NCTM. Reston, VA. https://www.amazon.com/Evaluate-Progress-Problem-Solving-NCTM/dp/0873532414
  • Chevallard, Y. (1989). On didactic transposition theory: Some Introductory Notes. Paper Presented at the International Symposium on Research and Development in Mathematics Education. Bratislava.
  • Chevallard, Y. (2013). Didactic Transposition in Mathematics Education. In Encyclopedies of Mathematics Education.
  • Clement, J. (2006). Designing classroom thought experiments: what we can learn from imagery indicators and expert protocols. NARST. SanFransisco. http://people.umass.edu/~clement/pdf/StephensClemDesignClssrmTE.pdf
  • Creswell, J. (2012). Research Design. Pustaka Pelajar.
  • David, H. (2015). The PISA Results in mathematics and science: A comparison between Israel and Turkey. Journal for the Education of Gifted Young Scientists, 3(1), 22-28.
  • Depdiknas. (2006). Kurikulum 2006: Standar Isi Mata Pelajaran Matematika untuk SMP/MTs. Ditjen Dikdasmen.
  • Diana, N., & Suryadi, D. (2020). Students ’ creative thinking skills on the circle subject in terms of learning obstacle and learning trajectory Students ’ creative thinking skills on the circle subject in terms of learning obstacle and learning trajectory. https://doi.org/10.1088/1742-6596/1521/3/032084
  • French, D. (2004). Teaching and Learning Geometry. Issues and Methods in Mathematical Education. London New York: Continuum., 119.
  • Gantert, A. X. (2008). Geometry. AMSCO School Publication, INC.
  • Gardner, H. (1983). Frames of mind. HarperCollins Publishers.
  • Getzels, Jacob W.; Jackson, P. W. (1962). Creativity and Intelligence: Explorations with Gifted Students. American Psychological Assosiation, 17, 293.
  • Hadi, S. dan Fauzan, A. (2003). Mengapa PMRI? Dalam Buletin PMRI (Pendidikan Matematika Realistik Indonesia). edisi I, J.
  • Harel, G. (2008). What Is Mathematics? A Pedagogical Answer to a Philosophical Question. ( PP 1-26) Washington: The Mathematical Association of America, Inc.
  • Hendriana, H & Sumarmo, U. (2014). nilaian Pembelajaran Matematika. Refika Aditaama.
  • Hodgson, T. (1995). “Connection as Problem-Solving Tools”, dalam Connecting Mathematics across the Curriculum. Editor: House, P.A. Dan Coxford, A.F. Reston, Virginia: NCTM.
  • Idris, N. (2011). The Impact of Using Geometers’ Sketchpad on Malaysia Students’ Achievement and Van Hiele Geometric Thingking Malaya. Journal for Mathematics Education Vol.2, No.2 Pp 94-107. University of Malaya, 2.
  • Johnson, K.M. dan Litynsky, C. L. (1995). Breathing Life into Mathematics, dalam Connecting Mathematics across the Curriculum. (V. N. Editor: House, P.A. dan Coxford, A.F. Reston (ed.)).
  • Kaur, B., & Lam, T. T. (2012). Reasoning, coummunication and connection in mathematics. World Scientific Publishing.
  • Kusmanto, H., & Marliyana, I. (2014). Pengaruh Pemahaman Matematika Terhadap Kemampuan Koneksi Matematika Siswa Kelas Vii Semester Genap Smp Negeri 2 Kasokandel Kabupaten Majalengka. Eduma : Mathematics Education Learning and Teaching, 3(2). https://doi.org/10.24235/eduma.v3i2.56
  • Lattery, M. (2001). Thought Experiments in PhysicsEducation: A Simple and Practical Example. Science and Education, 10(5), 485-92.
  • Lexy J. Moleong. (2011). Metodologi penelitian kualitatif. Bandung: Remaja Rosdakarya.
  • Maker, C. J. (1982). Curriculum development for the gifted. Rockville, Md.: Aspen Systems Corp.
  • Maker, C. J. (2004). Creativity and multiple intelligences: The DISCOVER project and research. In S. Lau, A. N. N. Hui, & G. Y. C. Ng (Eds.), Creativity: When East meets West. (pp. 341‐392). Singapore: World Scientific.
  • Maker, J., & Zimmerman, R., Alhusaini, A., & Pease, R. (2015). Real Engagement in Active Problem Solving (REAPS): An evidencebased model that meets content, process, product, and learning environment principles recommended for gifted students. APEX: The New Zealand Journal of Gifted Education, 19(1). Retrieved from www.giftedchildren.org.nz/apex.
  • Miles dan Huberman. (1992). Analisis data Kualitatif. Jakarta : UI Press.
  • Mousley, J. (2004). An aspect of mathematical understanding: the notion of “connected knowing”. Proceedings of the 28th Conference of the International Groupforthe Psychology of Mathematics Education, 3-25, 377-384.
  • NCTM. (2000). Principles and Standards for School Mathematics. www.nctm.org
  • Özgen, K. (2013). Self efficacy beliefs in mathematical literacy and connectiona between mathematics and real world : the case of high school students. Journal of International Education Research. 4(9).
  • Recegnova, M. (2005). Teaching of Analytic Geometry an vector calculus and proposals of problems’ solutions. ActaDidactica Universitatis Comenianae., Mathematics, Issue 5, 2005.
  • Romli, M. (2016). Profil Koneksi Matematis Siswa Perempuan SMA dengan Kemampuan Matematika Tinggi dalam Menyelesaikan Masalah Matematika. MUST: Journal of Mathematics Education, Science and Technology, 1(2), 144. https://doi.org/10.30651/must.v1i2.234
  • Saragih, M. . (2008). Rancangan dan Implementasi Program Perangkat Ajar serta Rancangan Materi Perangkat Ajar Geometri SMU Kelas I Berbantuan Komputer. Forum Penelitian Pendidikan, Thn 8.
  • Tortop, S. H. (2016). Why thought experiments should be used as an educational tool to develop problem solving skills and creativity of the gifted students. Journal of Gifted Educational and Creativity, 35-48.
  • Tortop, H. S. (2018). Üstün zekâlılar eğitiminde farklılaştırılmışöğretim, müfredat farklılaştırma modelleri [Differentiated instruction for gifted, curriculum differentiation models in gifted education]. Istanbul: Young Wise Publishing
  • Travers. (1987). Geometry. Laidlaw Brothers Publisher. River Forest Illinois.
  • Turmudi. (2010). Pembelajaran Matematika Kini dan Kencenderungan Masa Mendatang. Buku Bunga Rampai Pembelajaran MIPA, JICA FPMIPA.
  • Turnuklu, E., & Yesildere, S. (2007). The Pedagogical Content Knowledge in Mathematics: Pre-Service Primary Mathematics Teachers’ Perspectives in Turkey. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1(October), 1–13.
There are 42 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Differentiated Instruction
Authors

Nanang Diana 0000-0001-9458-1990

Didi Suryadi This is me 0000-0003-0871-8693

Jarnawi Afgani Dahlan This is me 0000-0002-9290-7755

Project Number 082340516464
Publication Date June 15, 2020
Published in Issue Year 2020

Cite

APA Diana, N., Suryadi, D., & Dahlan, J. A. (2020). Analysis of students’ mathematical connection abilities in solving problem of circle material: transposition study. Journal for the Education of Gifted Young Scientists, 8(2), 829-842. https://doi.org/10.17478/jegys.689673
AMA Diana N, Suryadi D, Dahlan JA. Analysis of students’ mathematical connection abilities in solving problem of circle material: transposition study. JEGYS. June 2020;8(2):829-842. doi:10.17478/jegys.689673
Chicago Diana, Nanang, Didi Suryadi, and Jarnawi Afgani Dahlan. “Analysis of students’ Mathematical Connection Abilities in Solving Problem of Circle Material: Transposition Study”. Journal for the Education of Gifted Young Scientists 8, no. 2 (June 2020): 829-42. https://doi.org/10.17478/jegys.689673.
EndNote Diana N, Suryadi D, Dahlan JA (June 1, 2020) Analysis of students’ mathematical connection abilities in solving problem of circle material: transposition study. Journal for the Education of Gifted Young Scientists 8 2 829–842.
IEEE N. Diana, D. Suryadi, and J. A. Dahlan, “Analysis of students’ mathematical connection abilities in solving problem of circle material: transposition study”, JEGYS, vol. 8, no. 2, pp. 829–842, 2020, doi: 10.17478/jegys.689673.
ISNAD Diana, Nanang et al. “Analysis of students’ Mathematical Connection Abilities in Solving Problem of Circle Material: Transposition Study”. Journal for the Education of Gifted Young Scientists 8/2 (June 2020), 829-842. https://doi.org/10.17478/jegys.689673.
JAMA Diana N, Suryadi D, Dahlan JA. Analysis of students’ mathematical connection abilities in solving problem of circle material: transposition study. JEGYS. 2020;8:829–842.
MLA Diana, Nanang et al. “Analysis of students’ Mathematical Connection Abilities in Solving Problem of Circle Material: Transposition Study”. Journal for the Education of Gifted Young Scientists, vol. 8, no. 2, 2020, pp. 829-42, doi:10.17478/jegys.689673.
Vancouver Diana N, Suryadi D, Dahlan JA. Analysis of students’ mathematical connection abilities in solving problem of circle material: transposition study. JEGYS. 2020;8(2):829-42.
By introducing the concept of the "Gifted Young Scientist," JEGYS has initiated a new research trend at the intersection of science-field education and gifted education.